Static wall layer formation



In cementing it is common to displace one yield stress fluid with another. As with many displacement flows, the displacement proceeds less efficiently at the walls than at the channel centre. Unlike other displacement flows, the yield stress of the displaced fluid can result residual layers at the walls that are wholly static. In the primary cementing context, these are layers of drilling mud that may remain in the well after the cement has been placed. During setting of the cement it is possible for contamination to occur, or for the mud layers to remain intact, but become dehydrated and form porous conduits along the well.

Various problems are of interest here and have been at least partially answered:

-         Will there be a static residual layer after a displacement?

-         What is the maximal thickness of static layer?

-         What is the likely thickness of the static layer?

-         How does the extent of the static layer vary with the shape of the duct?

-         How does the extent of the static layer vary with the process parameters, e.g. flow rate, fluid properties, etc… ?

-         What happens for example when trying to cement a washout?


Figure 1: Parallel multi-layer flow allowing static mud layers on the walls, existing far behind the displacement front. 




Figure 2:  Schematic of velocity and stress profiles that admit a static mud wall layer.

Figure 3: Contours of maximum static layer thickness,  plotted against spacer/slurry Bingham number and yield stress ratio. In the shaded area , and outside of this area, contours represent 5% of the slot width.


Relevant publications:


1.       M. Allouche, I.A. Frigaard & G. Sona, “Static wall layers in the displacement of two visco-plastic fluids in a plane slot.”, J. Fluid Mech. 424, pp. 243-277, (2000).

2.       I.A. Frigaard, O. Scherzer & G. Sona, “Uniqueness & non-uniqueness in the steady displacement of two visco-plastic fluids.” ZAMM, 81(2), pp. 99-118, (2001).

3.       I.A. Frigaard, M. Allouche & C. Gabard, “Incomplete Displacement of Viscoplastic Fluids in Slots and Pipes-Implications for Zonal Isolation.” Society of Petroleum Engineers paper number: SPE 64998, February (2001).

4.       I.A. Frigaard, M. Allouche & C. Gabard, “Setting rheological targets for chemical solutions in mud removal and cement slurry design.” Journal of Petroleum Technology, 53(8), pp. 65-66 (2001).

5.       I.A.Frigaard, S. Leimgruber and O. Scherzer, “Variational methods and maximal residual wall layers.”  J. Fluid Mechanics, 483, pp. 37-65, (2003).



-         M. Allouche

-         C. Gabard

-         I. Frigaard

-         S. Leimgruber

-         O. Scherzer

-         G. Sona

Contact: Ian Frigaard for more details